Microlens Research Articles

Morphological evolution mechanism of microstructures involved in shaping micro-pillar arrays into microlens arrays on fused silica surfaces by CO2 laser polishing

The periodic micro-pillars on the hard-brittle fused silica surface can be shaped into the smooth and defect-free microlens arrays (MLA) by CO2 laser polishing, which can be applied in imaging and beam-shaping. However, the morphology evolution mechanism of the micro-pillars is not clear during polishing, which seriously affects the rapid preparation of high-quality MLAs. Herein, a multi-physics coupling model is established to investigate the interaction between CO2 lasers and micro-pillars on the fused silica surface, and is verified from the perspectives of temporal and spatial temperature. The steady surface temperature evolution law with laser power and spot radius is explored, based on which, the parameter ‘Window’ for polishing is determined to make the material melt and flow without ablation removal. The morphology evolution of micro-pillars is investigated as well as laser-material interaction. It is found that under laser irradiation, the micro-pillar height first increases and then decreases, and its top curvature radius increases. The surface tension makes the dominant contributions to the melting and flow of the micro-pillar materials, while the Marangoni effect and the gravity have little effect. Furthermore, to fabricate the target MLAs with the specific dimensions, the influence of micro-pillar aspect ratio (φ) on microlens surface morphology is investigated. It is found that there are two critical φ for the target MLAs. For the required MLA with the target period of 200 μm and the target height of 40 μm, when the φ is larger than 5.1, the micro-pillar array fails to be shaped into the target MLA by CO2 laser polishing. As the φ decreases, the junction of micro-pillar and the substrate sags downwards significantly, and the deviation between the shaped- and the ideal spherical contours increases. To successfully prepared the target MLA and guarantee the geometry accuracy, the minimum φ is selected to be 0.71. This work has important theoretical significance for obtaining the smooth and defect-free target fused silica MLAs with the specific dimensions by CO2 laser non-evaporative polishing.

Axion star condensation around primordial black holes and microlensing limits

We present novel findings concerning the parameter space of axion stars, extended object forming in dense dark matter environments through gravitational condensation. We emphasize their formation within the dense minihalos that potentially surround primordial black holes and in axion miniclusters. Our study investigates the relation between the radius and mass of an axion star in these dense surroundings, revealing distinct morphological characteristics compared to isolated scenarios. We explore the implications of these results when applied to the bound state between a primordial black hole and an axion star and the gravitational microlensing from extended objects, leading to insights on the observational constraints from such “halo” axion stars. We provide a constraint on the fraction of the galactic population of axion stars from their contribution to the microlensing events from the EROS-2 survey, using the numerical resolution of the Schrödinger-Poisson equation.

A Study on the Effect of Microlens Arrays on the Correlated Color Temperature and Color Rendering Index of Quantum Dot Lighting

A Study on the Effect of Microlens Arrays on the Correlated Color Temperature and Color Rendering Index of Quantum Dot Lighting

Casting Light on Degeneracies: A Comprehensive Study of Lightcurve Variations in Microlensing Events OGLE-2017-BLG-0103 and OGLE-2017-BLG-0192

This study investigates orbital parallax in gravitational microlensing events, focusing on OGLE-2017-BLG-0103 and OGLE-2017-BLG-0192. For events with timescales ≤60 days, a Jerk-Parallax degeneracy arises due to high Jerk velocity ( vj˜ ), causing a fourfold continuous parallax degeneracy. OGLE-2017-BLG-0103, after incorporating orbital parallax, reveals four discrete degenerate parallax solutions, while OGLE-2017-BLG-0192 exhibits four discrete solutions without degeneracy. The asymmetric lightcurve of OGLE-2017-BLG-0103 suggests a more probable model where Xallarap is added to the parallax model, introducing tension. The galactic model analysis predicts a very low-mass stellar lens for OGLE-2017-BLG-0192. For OGLE-2017-BLG-0103, degenerate solutions suggest a low-mass star or a darker lens in the disk, while the Xallarap+Parallax model also predicts a stellar lens in the bulge, with the source being a solar-type star orbited by a dwarf star. This study presents five degenerate solutions for OGLE-2017-BLG-0103, emphasizing the potential for confirmation through high-resolution Adaptive Optics observations with Extremely Large Telescopes in the future. The complexities of degenerate scenarios in these microlensing events underscore the need to analyze special single-lens events in the Roman Telescope Era.

Design of a Novel Microlens Array and Imaging System for Light Fields.

Light field cameras are unsuitable for further acquisition of high-quality images due to their small depth of field, insufficient spatial resolution, and poor imaging quality. To address these issues, we proposed a novel four-focal-square microlens and light field system. A square aspheric microlens array with four orthogonal focal lengths was designed, in which the aperture of a single lens was 100 μm. The square arrangement improves pixel utilization, the four focal lengths increase the depth of field, and the aspheric improves image quality. The simulations demonstrate pixel utilization rates exceeding 90%, depth-of-field ranges 6.57 times that of a single focal length, and image quality is significantly improved. We have provided a potential solution for improving the depth of field and image quality of the light field imaging system.

Scheme of flash LiDAR employing glass aspherical microlens array with large field of illumination for autonomous vehicles

This study demonstrates a new scheme of flash LiDAR using a glass aspherical microlens array (MLA) to achieve a large field of illumination (FOI) for autonomous vehicles. A wider FOI of up to 100° was obtained. In contrast to a spherical MLA, the FOI is 38.9° which indicates that the proposed aspherical MLA is 2.6 times wider than the spherical MLA. The wider FOI achieved for the glass MLA is due to a novel laser drilling technique that produces conical micro-holes with a high aspect ratio (depth: diameter = 1.8:1), forming elliptical-like aspherical microlenses through wet etching. An FOI estimation model to provide theoretical basis for designing aspherical MLA with wider FOI is presented, which is in good agreement with experimental results. Furthermore, the optical efficiency of 90% for the FOI was calculated. In this study, we have proposed a unique laser drilling technique to produce glass aspherical MLA with wider FOI and higher optical efficiency for flash LiDAR use in autonomous vehicle applications.

Analytical form of the refocused images from correlation plenoptic imaging

Correlation plenoptic imaging (CPI) is emerging as a promising approach to light-field imaging (LFI), a technique for concurrently measuring light intensity distribution and propagation direction of light rays from a 3D scene. LFI thus enables single-shot 3D imaging, offering rapid volumetric reconstruction. The optical performance of traditional LFI, however, is limited by a micro-lens array, causing a decline in resolution as 3D capabilities improve. CPI overcomes these limitation by measuring photon number correlations on two photodetectors with spatial resolution, in a lenslet-free design, so that the correlation function can be decoded in post-processing to reconstruct high-resolution images. In this paper, we derive the analytical expression of CPI images reconstructed through refocusing, addressing the previously unknown mathematical relationship between object shape and its final image. We show that refocused images are not limited by numerical aperture-induced blurring, as in conventional imaging. Rather, the image features of CPI can be explained through an analogy with imaging systems illuminated by spatially coherent light.

Size and temperature effects on optoelectronic properties of Micro-LED arrays for display applications

In recent years, Micro-light-emitting diode (Micro-LED) has attracted much attention in the display field, because it provides the possibility of high pixel density, etc. The implementation of high pixel density is accompanied by the reduction of size, during which the performance degradation caused by sidewall defects gradually increases. At the same time, the increase in power density and difficulty in heat dissipation caused by high pixel density can also lead to poor thermal management, resulting in an increase in junction temperature, thus affecting the display effect. In this paper, we prepared seven different sizes of Micro-LED and studied the influence of size and temperature effects on the optoelectronic properties. Smaller-sized Micro-LED could withstand higher current densities because it was not affected by the current crowding effect. However, it tends to have a larger series resistance (RS) and a lower external quantum efficiency (EQE) due to sidewall defects created during etching. The luminance of the 100 μm and 7 μm Micro-LED was 340000 cd/m2 (at 83 A/cm2) and 32000 cd/m2 (at 773 A/cm2), respectively. The peak EQE of 100 μm Micro-LED was 16.87 %. On this basis, the temperature-dependence of the optoelectronic properties of 10 μm and 50 μm Micro-LED were studied. The larger the size of Micro-LED, the better the operational stability it exhibited. From the room temperature (RT) rose to 100 ℃, the EQE of the 10 μm and 50 μm Micro-LED decreased by 16 % and 13.1 %, respectively. These experimental results provide important data for the design and preparation of Micro-LED of different sizes and for exploring the operational stability at high temperatures.

DMD and microlens array as a switchable module for illumination angle scanning in optical diffraction tomography.

Optical diffraction tomography (ODT) enables label-free and morphological 3D imaging of biological samples using refractive-index (RI) contrast. To accomplish this, ODT systems typically capture multiple angular-specific scattering measurements, which are used to computationally reconstruct a sample's 3D RI. Standard ODT systems employ scanning mirrors to generate angular illuminations. However, scanning mirrors are limited to illuminating the sample from only one angle at a time. Furthermore, when operated at high speeds, these mirrors may exhibit mechanical instabilities that compromise image quality and measurement speed. Recently, newer ODT systems have been introduced that utilize digital-micromirror devices (DMD), spatial light modulators (SLMs), or LED arrays to achieve switchable angle-scanning with no physically-scanning components. However, these systems associate with power inefficiencies and/or spurious diffraction orders that can also limit imaging performance. In this work, we developed a novel non-interferometric ODT system that utilizes a fully switchable module for angle scanning composed of a DMD and microlens array (MLA). Compared to other switchable ODT systems, this module enables each illumination angle to be generated fully independently from every other illumination angle (i.e., no spurious diffraction orders) while also optimizing the power efficiency based on the required density of illumination angles. We validate the quantitative imaging capability of this system using calibration microspheres. We also demonstrate its capability for imaging multiple-scattering samples by imaging an early-stage zebrafish embryo.

Optical fibre based artificial compound eyes for direct static imaging and ultrafast motion detection

Natural selection has driven arthropods to evolve fantastic natural compound eyes (NCEs) with a unique anatomical structure, providing a promising blueprint for artificial compound eyes (ACEs) to achieve static and dynamic perceptions in complex environments. Specifically, each NCE utilises an array of ommatidia, the imaging units, distributed on a curved surface to enable abundant merits. This has inspired the development of many ACEs using various microlens arrays, but the reported ACEs have limited performances in static imaging and motion detection. Particularly, it is challenging to mimic the apposition modality to effectively transmit light rays collected by many microlenses on a curved surface to a flat imaging sensor chip while preserving their spatial relationships without interference. In this study, we integrate 271 lensed polymer optical fibres into a dome-like structure to faithfully mimic the structure of NCE. Our ACE has several parameters comparable to the NCEs: 271 ommatidia versus 272 for bark beetles, and 180o field of view (FOV) versus 150–180o FOV for most arthropods. In addition, our ACE outperforms the typical NCEs by ~100 times in dynamic response: 31.3 kHz versus 205 Hz for Glossina morsitans. Compared with other reported ACEs, our ACE enables real-time, 180o panoramic direct imaging and depth estimation within its nearly infinite depth of field. Moreover, our ACE can respond to an angular motion up to 5.6×106 deg/s with the ability to identify translation and rotation, making it suitable for applications to capture high-speed objects, such as surveillance, unmanned aerial/ground vehicles, and virtual reality.

Nondestructive Demolding of Structure-Designable High-Aspect-Ratio Nanoimprint Template.

Demolding is a crucial step in nanoimprint lithography (NIL) for successfully transferring template structures onto resist materials. The process, however, is often hindered by the adhesion and friction between the template and resist, leading to inevitable defects on the replicas and posing challenges in replicating templates with high-aspect-ratio (HAR) structures. Here, we introduce a novel approach using the dissolvable template method to achieve the nondestructive demolding of structure-designable HAR nanoimprint templates. The templates were fabricated by the 3D lithography technology, employing a positive photoresist that can be easily dissolved in alkaline solutions after exposure to ultraviolet (UV) radiation. By implementing this method, we successfully transferred dense arrays of pillars with a minimal diameter of 1.2 μm and a significant aspect ratio of 18, as well as a microlens array diffuser with randomly distributed structural parameters. The dissolvable template method paves the way for stress-free demolding, broadening NIL's application range.

The abundance of clustered primordial black holes from quasar microlensing

While elementary particles are the favored candidate for the elusive dark matter, primordial black holes (PBHs) have also been considered to fill that role. Gravitational microlensing is a very well-suited tool to detect and measure the abundance of compact objects in galaxies. Previous studies based on quasar microlensing exclude a significant presence of substellar to intermediate-mass black holes (BHs; $ 100M_ However, these studies were based on a spatially uniform distribution of BHs while, according to current theories of PBH formation, they are expected to appear in clusters. We study the impact of clustering in microlensing flux magnification, finding that at large scales clusters act like giant pseudo-particles, strongly affecting the emission coming from the broad-line region, which can no longer be used to define the zero microlensing baseline. As an alternative, we set this baseline from the intrinsic magnification ratios of quasar images predicted by macro lens models and compared them with the observed flux ratios in emission lines, infrared, and radio. The (magnitude) differences are the flux-ratio anomalies attributable to microlensing, which we estimate for 35 image pairs corresponding to 12 lens systems. A Bayesian analysis indicates that the observed anomalies are incompatible with the existence of a significant population of clustered PBHs. Furthermore, we find that more compact clusters exhibit a stronger microlensing impact. Consequently, we conclude that clustering makes the existence of a significant population of BHs in the substellar to intermediate mass range even more unlikely.

In Situ Dewetting Assisted Plasma Etching of Large‐Scale Uniform Nanocones on Arbitrarily Structured Glass Elements

AbstractNanocones are ideal for wide‐angle antireflection of glass elements, yet their applications often encounter complex geometries and large sizes, bringing serious difficulty in developing a reliable and efficient manufacturing process. Here, an in situ dewetting assisted plasma etching (In situ DAPE) method is proposed to engrave nanocones on arbitrarily structured glass elements in one step. While exposed to high‐energy plasma, pre‐sputtered platinum (Pt) film undergoes dewetting, forming uniformly distributed nanoparticles that act as in situ sacrificial masks for plasma etching to generate nanocones. The nanocone size is decided by nanoparticle size, which can be modified through the Marangoni effect of the melted Pt film. Incorporating a passivation step can improve the aspect ratio of nanocones up to ≈8:1 due to the trench effect. Nanocones with diameters ranging from 62 to 136 nm and heights from 126 to 942 nm can be achieved. The nanocones help to achieve an average transmittance of 98% over the 0.3–2.5 µm spectrum and a 79.4% laser‐induced damage threshold of bare fused silica. The efficient fabrication of nanocones over multiple glass elements is demonstrated including a 2‐inch flat window, cylindrical microlens array, and diffractive grating, highlighting the efficacy of the In situ DAPE method for high‐performance optical elements.

Imaging dark matter at the smallest scales with z ≈ 1 lensed stars

Recent observations of caustic-crossing galaxies at redshift 0.7 ≲ z ≲ 1 show a wealth of transient events. Most of them are believed to be microlensing events of highly magnified stars. Earlier work predicts such events should be common near the critical curves (CCs) of galaxy clusters (“near region”), but some are found relatively far away from these CCs (“far region”). We consider the possibility that substructure on milliarcsecond scales (few parsecs in the lens plane) is boosting the microlensing signal in the far region. We study the combined magnification from the macrolens, millilenses, and microlenses (“3M lensing”), when the macromodel magnification is relatively low (common in the far region). After considering realistic populations of millilenses and microlenses, we conclude that the enhanced microlensing rate around millilenses is not sufficient to explain the high fraction of observed events in the far region. Instead, we find that the shape of the luminosity function (LF) of the lensed stars combined with the amount of substructure in the lens plane determines the number of microlensing events found near and far from the CC. By measuring β (the exponent of the adopted power law LF, dN/dL = ϕ(L)∝(1/L)β), and the number density of microlensing events at each location, one can create a pseudoimage of the underlying distribution of mass on small scales. We identify two regimes: (i) positive-imaging regime where β > 2 and the number density of events is greater around substructures, and (ii) negative-imaging regime where β < 2 and the number density of microlensing events is reduced around substructures. This technique opens a new window to map the distribution of dark-matter substructure down to ∼103 M⊙. We study the particular case of seven microlensing events found in the Flashlights program in the Dragon arc (z = 0.725). A population of supergiant stars having a steep LF with β = 2.55−0.56+0.72 fits the distribution of these events in the far and near regions. We also find that the new microlensing events from JWST observations in this arc imply a surface mass density substructure of Σ∗ = 54 M⊙ pc−2, consistent with the expected population of stars from the intracluster medium. We identify a small region of high density of microlensing events, and interpret it as evidence of a possible invisible substructure, for which we derive a mass of ∼1.3 × 108 M⊙ (within its Einstein radius) in the galaxy cluster.

Efficient fabrication of large-scale chalcogenide glass microlens arrays via precision molding method

Infrared microlens arrays (IR MLAs) are crucial for infrared imaging, target detection, and night vision, but creating high-quality large-scale IR MLAs is costly and challenging. This study presents a precision molding method to produce 500 × 500 microlenses on chalcogenide glass. The method involves creating concave silica molds with femtosecond laser-assisted chemical etching, which are then used to press convex MLAs onto the chalcogenide glass surface. By using single-pulse direct writing technology, a microlens array template containing 500 × 500 microlenses can be completed within 25 min. Meanwhile, the chemical etching method offers a highly efficient and low-cost way to prepare mold. The resulting MLAs exhibited smooth surfaces, uniform structures, and good imaging and focusing capabilities, indicating the effectiveness of this approach for large-scale MLA patterning and batch production.

Influence of Black Hole Kick Velocity on Microlensing Distributions

The natal kick velocity distribution for black holes (BHs) is unknown regardless of its importance for understanding the BH formation process. Gravitational microlensing is a unique tool for studying the distribution of BHs in our Galaxy, and the first isolated stellar-mass BH event, OGLE-2011-BLG-0462/MOA-2011-BLG-191 (OB110462), was recently identified by astrometric microlensing. This study investigates how the natal kick velocity for Galactic BHs affects the microlensing event rate distribution. We consider a Maxwell distribution with various average kick velocities, as well as the consequent variation of the spatial distribution of BHs. We find that the event rate for the BH lenses toward the Galactic bulge decreases as v avg increases, mainly due to the scale height inflation. We focus on the unique microlensing parameters measured for OB110462, with microlens parallax π E larger than 0.06 for its long timescale of t E > 200 days. We calculate the expected number of BH events occurring with parameters similar to OB110462 during the OGLE-IV survey by Mróz et al. and compare it with the actual number that occurred, at least one. Our fiducial model predicts 0.52, 0.38, 0.18, 0.042, and 4.0 × 10−3 events occurring for v avg = 25, 50, 100, 200, and 400 km s−1, respectively, which suggests that the average kick velocity is likely to be v avg ≲ 100 km s−1. The expected number smaller than unity even at maximum might indicate our luck in finding OB110462, which can be tested with future surveys by, e.g., the Roman Space Telescope.

A New Parameterization for Finding Solutions for Microlensing Exoplanet Light Curves

The gravitational microlensing method of discovering exoplanets and multi-star systems can produce degenerate solutions, some of which require in-depth analysis to uncover. We propose a new parameter space that can be used to sample potential solutions more efficiently and is more robust at finding all degenerate solutions for the “central-resonant” caustic degeneracy. We identified two new parameters, k and h, that can be sampled in place of the mass ratios and separations of the systems under analysis to identify degenerate solutions. The parameter k is related to the size of the central caustic, Δξ c , while h is related to the distance of a point along the k contour from log(s) = 0, where s is the projected planet-host separation. In this work, we present the characteristics of these parameters and the tests we conducted to prove their efficacy.

Controllable Preparation of Fused Silica Micro Lens Array through Femtosecond Laser Penetration-Induced Modification Assisted Wet Etching.

As an integrable micro-optical device, micro lens arrays (MLAs) have significant applications in modern optical imaging, new energy technology, and advanced displays. In order to reduce the impact of laser modification on wet etching, we propose a technique of femtosecond laser penetration-induced modification-assisted wet etching (FLIPM-WE), which avoids the influence of previous modification layers on subsequent laser pulses and effectively improves the controllability of lens array preparation. We conducted a detailed study on the effects of the laser single pulse energy, pulse number, and hydrofluoric acid etching duration on the morphology of micro lenses and obtained the optimal process parameters. Ultimately, two types of fused silica micro lens arrays with different focal lengths but the same numerical aperture (NA = 0.458) were fabricated using the FLPIM-WE technology. Both arrays exhibited excellent geometric consistency and surface quality (Ra~30 nm). Moreover, they achieved clear imaging at various magnifications with an adjustment range of 1.3×~3.0×. This provides potential technical support for special micro-optical systems.

The impact of anodic mesh density and halogen anions on the optical characteristics of gradient refractive index microlens arrays fabricated in chalcohalide glass via microthermal poling

Gradient refractive index microlens arrays (GRIN MLAs), covering the visible to mid-infrared wavelength range, are imprinted in GeS2-Ga2S3-CsX (X = Cl, Br, and I) chalcohalide glasses by an efficient and economical microthermal poling process. This study investigates the impact of anodic mesh number (ranging from 400 to 2000 mesh) and halogen anions on the optical properties, including focal length, resolution, and aberration. Findings reveal that as the mesh number decreases, the focal length and aberration of GRIN MLAs increase. Optimal resolution is achieved with the 500 mesh sample, which also shows the best phase difference performance. The migration depth of Cs+ ions, influenced by halogen anions (from Cl to I), results in contrasting optical properties between lower mesh (400–750) and higher mesh (1000–2000) samples. Notably, the Cl-500 GRIN MLAs demonstrate a focal length of 615.0 μm, a maximum resolution of 6.35 lp/mm, and minimal aberration of −0.0591. These changes are attributed to the predominant transverse and longitudinal migration of Cs+ ions in mesh square areas. This research highlights the relationship between microthermal poling conditions, ion migration, and optical performance, providing valuable insights for the application of GRIN MLAs in advanced optical systems.

High-precision detection of laser focal position based on image processing forming by microlens array

High-precision detection of laser focal position based on image processing forming by microlens array